Eyes peering through slits in black masks, the commandos creep up the floors of the Baghdad apartment building, ready to pounce. Their target is Omar Tamimi, an insurgent believed to have carried out the January assassination of the governor of Baghdad province. In the past, the responsibility for such high-profile operations has been shouldered by teams of elite U.S. troops. But on this night, the American commandos are playing a support role to members of the new Iraqi army's Counter Terrorism Task Force, a unit the U.S. is training to take on more counterinsurgent dirty work. The early stages of the operation unfold
smoothly. One team of troops stops on the second floor, the other continues to
the third, where they place explosive charges against a thin wooden
apartment door. Two booms in quick succession echo in the concrete stairwell.
The doors shatter inward in a storm of wooden splinters, and the
Iraqi and American troops, identically outfitted with US-made M4 carbines,
night-vision goggles, boots, uniforms and body armor, burst in.

Inside the troops find children and three women, one of them elderly,
cowering on the floor. The Iraqi forces search the apartment and find
three men. They turn up Tamimi's identification papers, but not the target
himself. After cuffing the adultsincluding the womenwith plastic
ties, the Iraqi commander grills them about Tamimi, but gets
nowhere. Then an Iraqi officer begins chatting with the
children; before long one of them reveals that Tamimi had been in the apartment moments before the troops
rushed in. "He's still here," the officer tells the Americans. Soon a
Green Beret is heard yelling and laughing in the kitchen. Under the sink he'd
kicked a thin wall. Behind it was Tamimi, a thin sketch of a man,
curled into a ball.

Operations like the one that netted Tamimi earlier this year provide a glimpse
of what U.S. commanders hope will be the future of combat in Iraq.
Two years since the invasion of Iraq, the U.S. is scrambling to train and equip
a new Iraqi army to take over combat duties and pave the way for a
reduction in the size of the U.S. troop presence. After a slow start, the
training program appears to be picking up momentum: last week the
Pentagon announced plans to trim the number of U.S. troops in Iraq from 150,000
to 105,000 by early next year, a move that reflects the improved
capabilities of the Iraqi forces. The top commander of U.S. ground forces in
Iraq, Lt. Gen. John R. Vines, said that "very much sooner rather than
later, Iraq will be able to provide for its own security."

The Iraqi special-ops units like the one that captured Tamimi are spearheading
that push. TIME was recently granted access to the Iraqi
commandos and their U.S. advisors, observed their training sessions and
accompanied the units on patrol. While their
numbers are few, Iraqi special forces have assumed a bigger role in sensitive
counter-insurgent operations, often acting as the lead teams in raids
and rescue missions. In some cases, Iraqi units have used intelligence gleaned
from locals to identify their own low-level targets, and then
execute small raids on their own. Trained by Task Force Pioneer, a unit drawn
from a support company from the U.S. Special Operating Force's 10th
Group, the emerging Iraqi commando units have impressed U.S. commanders with
their combat performance and bolstered confidence that Iraqis can keep
the insurgents at bay on their own. "We can step away more now," says the U.S.
commander of Task Force Pioneer, who, like all of the special forces
in this story, cannot be named. "It's about 50-50."

That said, the U.S. hasn't yet ceded command and control to the Iraqis. "We
train the rank-and-file but we're the leadership," says the Pioneer
commander. However well-trained, the Iraqi special forces comprise only a tiny
fraction of the 57,000-member Iraqi army, which has been plagued by
low morale, inconsistent training and infiltration by insurgents.

But the U.S. hopes the commandos provide a
model for improvement. Over the past year the ISOF units have conducted 538 combat missions,
capturing 431 suspected insurgents, over 1,700 weapons and tons of
munitions. They've seen bloody action in the battles for Najaf, Samarra and
Fallujah, and have fought insurgents in Ramadi and Baghdad. Among the
Iraqis' biggest successes were the capture of militants involved in the April
2004 attack in Fallujah on four U.S.
security contractors; and they killed an insurgent suspected of involvement in
the beheading last May of American Nicholas Berg. Advisors from the
U.S. Green Berets say the Iraqi special-ops teams have suffered none of the
problems of desertion in the face of enemy fire seen in most of the
regular Iraqi units. None have
refused to fight, they say, and rates of those absent without leave are
well below other forces. "It's unbelievable, but it's all down to the espirit
de corps," says the Americans' Executive Officer.

Putting Iraqis on the front lines, U.S. officials say, is yielding results in
the shadow war against the insurgents. When the key to unraveling
insurgencies is denying the rebels the support of the population, putting an
Iraqi face on the offensives is vital. It also helps avoid blunders.
Often targeting information is slightly off, with troops raiding the wrong
house. Local Iraqis are loath to point the Americans in the right
direction. "They're not scared of Americans, but when an Iraqi in a ski mask
confronts them they talk a lot more, and they're more likely to say,
'He's not here but lives across the road,'" says Task Force Pioneer's
commander. During the raid on Tamimi's safehouse, the joint U.S.-Iraqi team
hauled off Tamimi and another insurgent suspected of being a key bombmaker. The
other men upstairs were left behind, a mark of the more "surgical"
style of business the Green Berets are hoping the Iraqis can deliver them,
blunting locals' perceptions of Americans as brutish and arbitrary. "In
the past, we'd have scooped them all up," says an
American with the CTF, "but we only took the guys our Iraqis said were
dirty.